June 5, 2024, 4:44 a.m. | Jingcheng Liu, Jalaj Upadhyay, Zongrui Zou

cs.LG updates on arXiv.org arxiv.org

arXiv:2406.02140v1 Announce Type: cross
Abstract: In this paper, we introduce the $\ell_p^p$-error metric (for $p \geq 2$) when answering linear queries under the constraint of differential privacy. We characterize such an error under $(\epsilon,\delta)$-differential privacy. Before this paper, tight characterization in the hardness of privately answering linear queries was known under $\ell_2^2$-error metric (Edmonds et al., STOC 2020) and $\ell_p^2$-error metric for unbiased mechanisms (Nikolov and Tang, ITCS 2024). As a direct consequence of our results, we give tight bounds …

abstract arxiv cs.cr cs.lg delta differential differential privacy epsilon error linear matrix paper privacy queries type

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